Finding Third Root & Values of p & q

[chudzoik]

Homework Statement

Given that 2 is a repeated root of the equation 2x^3 + px^2 + qx -4 = 0, find the third root and the values of p and q.

Homework Equations

b^2 - 4ac(?)

The Attempt at a Solution

Since it said 2 is a root I plugged in 2 as the value of x and rearranged the equation in terms of q, which I figured out to be q = -2(3+p), but when I plug that back into the original equation to try and find p, I got 16 + 4p - 12 - 4p - 4 = 0. The p's cancel out so I don't know if I think I've done something wrong.

 

[micromass]

If you know about derivatives (which I assume you don't, since you posted in precalc): what do you know about the derivative if the original polynomial has a repeated root??

If you do not know about derivatives: note that if 2 is a repeated root, then your original polynomial can be written as $2(x-2)^2(x-c)$ for a certain c. Work that out and compare it to the original polynomial.

 

[Mark44]

If you know about derivatives (which I assume you don't, since you posted in precalc): what do you know about the derivative if the original polynomial has a repeated root??

If you do not know about derivatives: note that if 2 is a repeated root, then your original polynomial can be written as $2(x-2)^2(x-c)$ for a certain c. Work that out and compare it to the original polynomial.

The OP posted in the calculus section, also, but I deleted it there. This seems to me to be a problem that doesn't require calculus.

 

[chudzoik]

If you know about derivatives (which I assume you don't, since you posted in precalc): what do you know about the derivative if the original polynomial has a repeated root??

If you do not know about derivatives: note that if 2 is a repeated root, then your original polynomial can be written as $2(x-2)^2(x-c)$ for a certain c. Work that out and compare it to the original polynomial.

Where does c come from and what does "certain c" mean exactly?

 

[Mark44]

c is the third root that you're trying to find. "For certain c" means that we don't know exactly what that number is, but we know that the 3rd degree polynomial with a repeated root of 2 has to factor into 2(x - 2)²(x - c) for some real number c.